Are there any other ways of decomposing 1/11 into sum of two unit fractions? In how many ways can we write 1/60 ass a sum of two unit fractions? More generally, in how many ways can the unit fraction 1/n be written as the sum of two unit fractions? In other word, how many ordered pairs (a, b) of positive integers a, b are there for which 1/n = 1/a + 1/b?
Are there any other ways of decomposing 1/11 into sum of two unit fractions? In how many ways can we write 1/60 ass a sum of two unit fractions? More generally, in how many ways can the unit fraction 1/n be written as the sum of two unit fractions? In other word, how many ordered pairs (a, b) of positive integers a, b are there for which 1/n = 1/a + 1/b?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
A unit fraction is a fraction of the form 1/n where n is a positive integer. Note that the unit fraction can be written as the sum of two fractions in the following three ways:
1/11 = (1/12) + (1/132) = (1/22) + (1/22) = (1/132) + (1/12)
Are there any other ways of decomposing 1/11 into sum of two unit fractions? In how many ways can we write 1/60 ass a sum of two unit fractions? More generally, in how many ways can the unit fraction 1/n be written as the sum of two unit fractions? In other word, how many ordered pairs (a, b) of positive integers a, b are there for which
1/n = 1/a + 1/b?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,